Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. (English) Zbl 0659.65132

Osher, Stanley; Sethian, James A.

J. Comput. Phys. 79, No. 1, 12-49 (1988).

New methodologies are formulated for following fronts propagating with curvature-dependent speed, which models, among other things, crystal growth and flame propagation. The algoritms are based on an approximation of the Hamilton-Jacobi formulations for such problems. The paper is carefully written with numerical exemplification (including detailed graphics) which shows that the numerical schemes accurately capture the formation of sharp gradients and cusps in the moving fronts.

Reviewer: R.S.Anderssen

MSC:

65Z05	Applications to the sciences
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35L65	Hyperbolic conservation laws
80A25	Combustion
82D25	Statistical mechanics of crystals

Keywords:

hyperbolic conservation laws; numerical example; following fronts propagating; curvature-dependent speed; crystal growth; flame propagation; Hamilton-Jacobi formulations; moving fronts

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